Not really sure what I should do to improve this team. I'm in 7th place out of 13 teams in a 5x5 roto league (keep 5 each year). My offense is the second best and (needless to say) my pitching sucks. Should I trade away some offense, or be patient with my SPs? I'm also thinking of trying to upgrade my offense at certain positions (3B or SS especially) by trading away pitching.

Upgrading your infield would cost you too much and you'd end up even lower in the standings. Here's what I would do:
1. Your biggest hitting hole is 3B with Chavez. Thankfully it's a very deep position. Is Edwin Encarnacion still available? I know many managers bailed on him after his crummy start, but I see him as returning to form so go check it out.
2. Option 2 is to plug Glaus at 3B and scour the FA/WW for a SS. Peralta still there?
3. I'd definately try and deal the following players: Chavez, Tracy, Green, DeJesus, Burnett, Moyer. Go for SPs, quality ones. If you can land 1-2 quality SPs and maintain your lineup, you'll be cruising.

Troy Glaus is a solid SS, not elite but he will get you HRs and RBI assuming he stays healthy. Your offense is fine. And your pitching isn't that bad. Zambrano has been off to a rough start but will rebound and I expect johnson to have a pretty solid year. Felix (cross your fingers) had sick stuff to start the year and we (as you know, i have him on my team too) can only hope that he's okay and comes back looking the same. Your main weak spot, I think, is your relief pitching, but I'm not entirely sure what to tell you without knowing your league's scoring categories...or who is still available in your league. If Jhonny Peralta is still available, snatch him up and plug him in at SS and move Glaus to 3rd...that would be a better lineup than having eric chavez in there...